Question

Please help on this calculus question?

find the critical values of f, describe the open intervals on which f is increasing or decreasing, and locate all relative extrema.
f(x)=x^2+8x+10

I got as far as the derivative: f'(x)=2x+8
and factor that out to 2(x+4)

so are -4 and -2 critical values?

Answer 1

Since the derivative is linear (the highest term is x¹, or just x), there's only one zero, at x=-4

Answer 2

critical value is x=-4
\[f \prime \prime \left( x \right)=2,at x=4,f \prime \prime \left( x \right)=2>0,\]
there is minima x=-4

Answer 3

ok. so there is no maximum

Answer 4

?

Answer 5

and how do I find the increase and decrease?

Answer 6

it is increasing if f'(x)>0
or 2(x+4)>0,x>-4
including end points f(x) is increasing in [-4,infty )
similarly it is decreasing if f'(x)<0
now you can calculate .

Answer 7

so decrease in on [infty,-4)

Answer 8

infinity is always open interval.
-infinity <-4
interval is including end points (- infinity,-4]

Answer 9

Ah ok. thank you so much

Answer 10

yw